The BestBeer Inc. is also considering developing a new mango$-$flavored beer. The initial investment is $$100,000$ to develop the product and get ready for production. The calculated material and labor cost is $$0\mathrm{.}50$ per bottle. The whole sale price is set at $$1\mathrm{.}50.$

What is the fixed cost?

What is the unit variable cost?

What is the unit margin in $$?$ In $\%?$

What is the break$-$even quantity for offering this new flavored beer?

If the company hopes to reduce the break$-$even quantity by half without changing any other numbers except price, how much they should charge?

If BestBeer Inc. decided to offer a $20\%$ discount on the wholesale price, what would be the new break$-$even quantity? What is the percentage change of the break$-$even quantity, as comparing to the case without the discount?